Method and apparatus for monitoring fluid dynamic drag

ABSTRACT

Methods and apparatus for monitoring fluid-dynamic drag on an object, such as a bicycle, ground vehicle, watercraft, aircraft, or portion of a wind turbine are provided. An array of sensors obtain sensor readings for example indicating: power input for propelling the object; air speed and direction relative to motion of the object; and ground speed of the object. Sensor readings may also indicate: temperature; elevation and humidity for providing a measurement of air density. Sensor readings may also indicate inclination angle and forward acceleration. Processing circuitry determines a coefficient of drag area based on the sensor readings and optionally one or more stored parameters, according to a predetermined relationship. A pitot tube based apparatus for measuring fluid speed and direction is also provided. Methods for dynamic in situ calibration of the pitot tube apparatus, and of adjusting correction factors applied to correct measurement errors of this apparatus are also provided.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of Ser. No. 16/302,768, filed Nov.19, 2018, which claims priority to international application no.PCT/CA2017/050604 filed May 18, 2017, which claims the benefit ofprovisional application No. 62/338,859 filed on May 19, 2016, all ofwhich are incorporated by reference in their entireties.

FIELD OF THE INVENTION

The present invention pertains to the field of aerodynamic measurementand in particular to a method and apparatus for monitoring fluid-dynamic(e.g. aerodynamic) drag on an object using an array of sensors.

BACKGROUND

One of the most sought out quantities in aerodynamic performancemeasurements of human powered vehicles (e.g., a bicycle) is the dragforce acting on the vehicle. Under controlled conditions of high qualitylow speed wind tunnel facilities, it is possible to perform suchmeasurements in order to find the most suitable vehicle and bodyposition for minimal aerodynamic drag. Aerodynamic analysis of otherobjects, such as but not limited to ground-based and airborne vehicles,can be similarly performed.

U.S. Pat. No. 8,612,165 discloses a method and system for measuringaerodynamic properties of objects, including determining the dependenceof a drag area of an object upon airflow yaw angle and direction.However, this approach requires data to be collected over an entirevehicle trip and analyzed by the computation of multiple virtualelevation profiles to determine a “best fitting” relationship betweenaerodynamic drag area and airflow yaw angle.

International Patent Application Publication No. WO 2007/038278discloses an apparatus for measuring static and dynamic pressure andspeed and acceleration of a vehicle, in order to calculate powerexpended to move the vehicle. However, the relationship between wind yawangle and aerodynamic drag is not fully considered. In addition, thedisclosed approach does not adequately accommodate aggressive cross-windscenarios, or conditions where the vehicle is undergoing significantaccelerations or decelerations.

U.S. Pat. No. 9,188,496 discloses a system and method of calculatingunder changing conditions in real-time aerodynamic drag acting on arider on a vehicle. However, this methodology and application relies onreal-time analysis of one or more force sensors at points of contactbetween the rider and the vehicle and does not attempt to provide ameasurement of wind speed and wind yaw angle.

Therefore there is a need for a method and apparatus for monitoringand/or determining fluid-dynamic (e.g. aerodynamic) drag on an object,using sensors, that is not subject to one or more limitations of theprior art.

This background information is provided to reveal information believedby the applicant to be of possible relevance to the present invention.No admission is necessarily intended, nor should be construed, that anyof the preceding information constitutes prior art against the presentinvention.

SUMMARY

An object of embodiments of the present invention is to provide a methodand apparatus for monitoring fluid-dynamic (e.g. aerodynamic) drag on anobject, such as a bicycle or other ground vehicle powered by a human orother power source, airborne vehicles, watercraft, remote controlvehicles, wind turbines, or other objects moving relative to an ambientfluid. In accordance with embodiments of the present invention, there isprovided a method for determining fluid-dynamic drag on an object,comprising: obtaining sensor readings indicative of: power input forpropelling the object; air/fluid speed and direction relative to theobject; and speed and direction of the object in a fixed reference frame(e.g. ground speed and direction); and determining, using a computer, acoefficient of drag area based on the sensor readings and optionally oneor more stored parameters, according to a predetermined relationship.Optionally, the sensor readings are further indicative of one or moreof: temperature; elevation and humidity, said sensor readings oftemperature, elevation and humidity combined to provide a measurement ofair/fluid density. Optionally, the sensor readings are furtherindicative of inclination angle and forward acceleration, and whereinthe stored parameters are indicative of at least weight or mass of theobject plus load carried thereby.

In accordance with embodiments of the present invention, there isprovided an apparatus for determining fluid-dynamic drag on an object,comprising: a set of sensors configured to provide sensor readingsindicative of: power input for propelling the object; air speed anddirection relative to the object; and speed and direction of the objectin a given reference frame; and a processor operatively coupled to theset of sensors and to a memory, the processor configured to determine acoefficient of drag area based on the sensor readings and optionally oneor more stored parameters, according to a predetermined relationship;and an interface configured to provide the determined coefficient ofdrag area to a user.

In accordance with embodiments of the present invention, there isprovided an apparatus for measuring fluid speed and direction,comprising: a multi-hole pitot probe whose basic calibration iscompleted using wind tunnel measurements and adjustments to thecalibration for each device are applied in-situ using a pre-definedalgorithm.

In accordance with embodiments of the present invention, there isprovided a method for determining fluid dynamic drag on an object,comprising: obtaining sensor readings from one or a combination ofsensors, the sensor readings indicative of external thrust forces and/orresistive forces applied to the object; and determining, using acomputer, a coefficient of drag area based on the sensor readings andoptionally one or more stored parameters, according to a predeterminedrelationship.

In accordance with embodiments of the present invention, there isprovided an apparatus for determining fluid-dynamic drag on an object,comprising: a set of sensors configured to provide sensor readingsindicative of external thrust forces and/or resistive forces applied tothe object; and processing circuitry operatively coupled to the set ofsensors, the processing circuitry configured to determine a coefficientof drag area based on the sensor readings and optionally one or morestored parameters, according to a predetermined relationship; and aninterface configured to provide the determined coefficient of drag areato a user.

In accordance with embodiments of the present invention, there isprovided an apparatus for measuring fluid speed and direction,comprising: at least a first pitot tube, a second pitot tube and a thirdpitot tube, each pitot tube having a respective pressure port, thepressure ports facing in different directions; a first differentialpressure transducer operatively coupled to the first pitot tube and thesecond pitot tube for providing a first measurement of differentialpressure between the first pitot tube and the second pilot tube; and asecond differential pressure transducer operatively coupled to the firstpitot tube and the third pitot tube for providing a second measurementof differential pressure between the first pitot tube and the thirdpitot tube.

In accordance with embodiments of the present invention, there isprovided a method for calibrating a multi-hole pitot probe wind sensor,comprising: receiving an indication of a body proximate to the probe;estimating a flow field induced by the presence of the body at least inthe vicinity of the probe; performing computations related to asuperposition of the estimated flow field onto another flow field forthe probe; estimating a measurement error induced in the probe by thebody, the estimate based on the superposition; and providing acorrection factor for at least partially countering the measurementerror.

In accordance with embodiments of the present invention, there isprovided a method for calibrating a multi-hole pitot probe wind sensor,comprising: providing a set of one or more configurations for a bodyproximate to the probe; for each of the set of configurations,experimentally determining a measurement error induced in the probe bythe body and providing a correction factor for at least partiallycountering the measurement error.

In accordance with embodiments of the present invention, there isprovided a method for operating a multi-hole pitot probe wind sensor,comprising: receiving an indication of relative location and/or shape ofa body proximate to the probe; and providing a correction factor to beapplied to measurements from the probe based on the received indication.

In accordance with embodiments of the present invention, there isprovided an apparatus for determining rolling resistance exerted by asurface on a wheeled object, the apparatus comprising: a vibrationsensor configured to measure vibrations due to rolling of the wheeledobject on the surface; processing circuitry operatively coupled to thevibration sensor, the processing circuitry configured to determine acoefficient of rolling resistance based on the measured vibrations andone or more stored parameters, according to a predeterminedrelationship.

In accordance with embodiments of the present invention, there isprovided a method for determining rolling resistance exerted by asurface on a wheeled object, the method comprising: measuring, using avibration sensor, vibrations due to rolling of the wheeled object on thesurface; determining, using a computer, a coefficient of rollingresistance based on the measured vibrations and one or more storedparameters, according to a predetermined relationship.

BRIEF DESCRIPTION OF THE FIGURES

Further features and advantages of the present invention will becomeapparent from the following detailed description, taken in combinationwith the appended drawings, in which:

FIG. 1 schematically illustrates an apparatus according to an embodimentof the present invention.

FIG. 2 illustrates yaw, pitch, and roll directions according to anembodiment of the present invention.

FIGS. 3A to 3F illustrate views of an apparatus provided according to anembodiment of the present invention.

FIG. 4 illustrates a block diagram showing force relationships accordingto an embodiment of the present invention.

FIG. 5 illustrates a block diagram showing force relationships accordingto another embodiment of the present invention.

FIG. 6 illustrates an apparatus comprising pressure transducers used asa wind speed and yaw angle sensor, according to an embodiment of thepresent invention.

FIG. 7 illustrates operation of a wind speed and yaw angle sensoraccording to an embodiment of the present invention.

FIGS. 8A and 8B illustrate test data showing a correlation between poweroutput and drag according to an embodiment of the present invention.

FIGS. 9A and 9B illustrate additional test data showing variation inestimated and measured input power and velocity over time, according toan embodiment of the present invention.

FIG. 10 illustrates a method for determining fluid dynamic drag on anobject, in accordance with an embodiment of the present invention.

FIG. 11 illustrates a method for calibrating a multi-hole pitot probewind sensor, in accordance with an embodiment of the present invention.

FIG. 12 illustrates a method for calibrating a multi-hole pitot probewind sensor, in accordance with another embodiment of the presentinvention.

FIG. 13 illustrates a method for operating a multi-hole pitot probe windsensor, in accordance with an embodiment of the present invention.

FIG. 14 illustrates a method for determining rolling resistance exertedby a surface on a wheeled object, in accordance with an embodiment ofthe present invention.

It will be noted that throughout the appended drawings, like featuresare identified by like reference numerals.

DETAILED DESCRIPTION

Embodiments of the present invention provide a field-based fluid-dynamic(e.g. aerodynamic) measurement method and apparatus in which sensorsmounted on an object are used to register information on the object'sfluid-dynamic performance. The information may be registered in realtime and updated as conditions change. Output from the sensors is usedat least in part to estimate the resistance caused by fluid-dynamic dragon the object in real-time. The object may be a human-powered vehiclesuch as a bicycle, or another object of interest which moves relative toa fluid such as air. Although the term “air” is used herein, it shouldbe readily understood that air can refer to one of a variety of fluidmedia through which an object can move, such as a gaseous or possiblyliquid fluid medium.

For a human-powered vehicle such as a bicycle, this allows informationto be gathered on fluid-dynamic performance for a variety of human bodypositions. Such information is useful because the human body positionpresenting the least drag is not necessarily the same position whichallows the most efficient power production for driving the vehicle. Bycomparing power and fluid-dynamic information for different bodypositions, desirable trade-offs between power and drag can be found.

Embodiments of the present invention employ a wind measurement devicewhich simultaneously determines wind yaw angle and wind speed magnitude.Direct force power meter measurements are used as one of a plurality ofinputs for computing estimated fluid-dynamic drag coefficients. Invarious embodiments, rather than estimating the input power to thevehicle using on-board sensors, vehicle driving power is measureddirectly via sensors such as strain gauge sensors. Fluid-dynamic drag isthen estimated using this power measurement.

Embodiments of the present invention obtain and use measurements of windmagnitude, wind yaw angle, road slope, vehicle acceleration, vehiclespeed and direction in a given reference frame (e.g. ground speed anddirection), rolling resistance estimate, drivetrain resistance estimate,vehicle and passenger weight, vehicle and passenger position estimates,and vehicle input power. The measurements are combined together toestimate the fluid-dynamic drag of the vehicle.

Embodiments of the present invention provide for and utilize aparticular design of a three-hole, or five-hole pitot tube sensor fordirectly measuring wind speed and wind yaw angle. However, it is notedthat other embodiments of the present invention can provide foralternative multi-hole probe technologies in place of this particulardesign. In one embodiment of the present invention the multi-hole probeis configured to provide omnidirectional wind speed measurement andheading.

Embodiments of the present invention provide for and utilize acombination of vibration or accelerometer sensors and pressure sensors(with knowledge of vehicle weight and tire type) for the detection ofinstantaneous changes in road surface condition and associated rollingresistance coefficients.

Embodiments of the present invention provide for and utilize acombination of humidity sensors, temperature sensors, and heart ratesensors for estimation of metabolic function, specifically sweat rate,electrolyte loss, and net fluid loss of a human providing driving powerof a vehicle such as a bicycle. Alternative sensors indicative of sweatrate, heart rate, or the like, or a combination thereof, may be used tofacilitate estimates of metabolic performance. As such, embodiments ofthe present invention relate to monitoring metabolic performance of aperson powering a vehicle, including acquiring and processing relevantsensor measurements.

Embodiments of the present invention provide for a sensing and computingdevice that may be integrated into existing technology of human poweredvehicles. For example, a cycling computer can be provided which, inaddition to recording parameters such as speed, cadence, heart rate,elevation, temperature, input power, and heading, also obtains sensorinformation for providing instantaneous or near-instantaneous estimatesof the aerodynamic drag force exerted on the vehicle in combination withthe rider.

Embodiments of the present invention provide for a method determiningfluid-dynamic drag on an object. The method includes obtaining data fromone or more sensors and processing the data using processing circuitry.The processing circuitry can include, for example, a computermicroprocessor, digital or analog processing circuitry for example asembodied in an application specific integrated circuit, or anothercomputing device.

Embodiments of the present invention provide a method for calibrating amulti-hole pitot probe wind sensor. The calibration is in situcalibration. The method includes receiving an indication of presenceand/or location of a body proximate to the probe. The body may be ahuman body or other object. The indication may be provided in the formof input parameters provided by a user, via signals from one or moreproximity sensors or other sensors (e.g., sensors embedded in or affixedto the human body), or a combination thereof. The method furtherincludes estimating a flow field induced by the presence of the body atleast in the vicinity of the probe. The estimate may be made based on ananalytical fluid flow model and/or experimental data, for example. Themethod further includes performing computations related to asuperposition of the estimated flow field onto another flow field forthe probe itself. The flow field for the probe is descriptive of airflow around the probe in absence of the body. The flow field for theprobe may be predetermined based on analytical modelling and/or priorwind tunnel experiments. The method further includes estimating ameasurement error induced in the probe by the body, the estimate basedon the superposition. The method further includes providing a correctionfactor for at least partially countering the measurement error.

The calibration may be performed for various positions and/orconfigurations of the body. For example, when the position and/or shapeof the body relative to the sensor is detected using proximity sensors,the calibration may be performed for multiple different sensor readingsor ranges of sensor readings.

Embodiments of the present invention provide a method for operating amulti-hole pitot probe wind sensor following calibration as performedabove, or in another manner for example via field-based measurements.The method includes receiving an indication of relative location and/orshape of a body proximate to the probe. The method further includesadjusting a correction factor to be applied to the probe measurementsbased on the received indication. The correction factors may bedetermined based at least partially on pre-calibration. The indicationmay be based on output of proximity sensors, or via another means suchas user input.

Embodiments of the present invention provide a method for calibrating amulti-hole pitot probe wind sensor. The method includes providing a setof one or more configurations for a body proximate to the probe. Themethod further includes, for each of the set of configurations,experimentally determining a measurement error induced in the probe bythe body and providing a correction factor for at least partiallycountering the measurement error. In some embodiments, the set of one ormore configurations are detected using one or more proximity sensors.

Embodiments of the present invention provide a multi-hole pitot probewind sensor. The sensor includes at least a first pitot tube, a secondpitot tube and a third pitot tube. Each pitot tube has a respectivepressure port, and the pressure ports face in different directions. Thesensor also includes two differential pressure transducers. The firstdifferential pressure transducer is operatively coupled to the firstpitot tube and the second pitot tube for providing a first measurementof differential pressure between the first pitot tube and the secondpitot tube. The second differential pressure transducer is operativelycoupled to the first pitot tube and the third pitot tube for providing asecond measurement of differential pressure between the first pitot tubeand the third pitot tube.

Embodiments of the present invention provide for an apparatus whichdirectly measures wind yaw angle effects, Reynolds number effects, roadsurface condition effects, and inertial effects on aerodynamicperformance.

Embodiments of the present invention may be applied for testing riderfluid-dynamic performance using different body positions. Embodiments ofthe present invention may be applied for obtaining environmental data ona specific race course: including wind, temperature, humidity,elevation. Embodiments of the present invention may be applied fortraining athletes in optimal drafting techniques. Embodiments of thepresent invention may be applied for new-athlete-specific assessments ofride difficulty.

System Description

FIG. 1 illustrates a sensing and computing apparatus provided accordingto an embodiment of the present invention. The apparatus is presented inthe context of a bicycle, although it can be readily adapted to otherapplications. The apparatus includes multiple sensors providing input toa microprocessor 110 operatively coupled to memory 112, and an interfacedevice 115 for presenting information to a user. In one embodiment, allof the illustrated sensors are included. In other embodiments, one ormore of the sensors may be omitted, potentially with a correspondingloss of function. When a sensor is omitted, the data typically providedby the sensor may be estimated, for example as a fixed value or as afunction of other sensor inputs according to a predeterminedrelationship. It will be readily understood which sensors are requiredfor providing a given functionality of the apparatus. In someembodiments, at least some of the sensors are provided within a commonhousing, along with the microprocessor. The microprocessor can bereplaced with other processing circuitry in some embodiments.

At least some of the sensors, along with the processing circuitry,memory and interface device (prior to configuration as describedherein), may be provided as off-the-shelf components, which may beparticularly configured to operate as described herein. In particular,the pressure transducers may be particularly configured as describedherein.

The sensors include an accelerometer and/or gyroscope 120 configured tomeasure forward acceleration, roll angle, handlebar yaw, and/or pitchangle. Pitch angle may correspond to the slope or grade of the roadsurface. FIG. 2 illustrates definitions of yaw, pitch and rollparameters for a bicycle, by way of example.

The sensors include a relative humidity sensor 125 configured to measurewater vapor (or other vapor and/or particle) concentration in air. Airdensity is significantly impacted by humidity, and air density is arelevant parameter for computing drag forces in air. Therefore, inputfrom the relative humidity sensor may be used to determine air densityand adjust drag force values during computation. The processingcircuitry may be configured to compute drag force coefficients based atleast in part on relative humidity as indicative of air density.

The sensors include a barometric pressure sensor 130. The barometricpressure is used as a reference pressure in wind speed calculations. Thebarometric pressure may also operate as an altimeter used to computelocal elevation. Computing of elevation based on barometric pressurewill be readily understood by a worker skilled in the art. The changesin elevation over time may be used to compute road slope and support themeasurements from the accelerometer and/or gyroscope 120.

In some embodiments, the reference pressure can be readily obtainedusing a static pitot tube based pressure sensor affixed to the object orvehicle.

The sensors include a temperature sensor 135. Temperature measurementsmay be used to facilitate determining air density as a function of localair temperature. Temperature and elevation measurements may be is usedin conjunction with the relative humidity sensor 125 to estimate the airdensity.

The sensors include a vibration sensor 140, for example incorporating apiezoelectric transducer. The vibration sensor measures local vibrationof the vehicle or object itself. Input from the vibration sensor may beused, by the processing circuitry, to dynamically estimate rollingfriction caused by the vehicle tires according to a predeterminedquantitative relationship. Rolling friction measurements may be based inpart on additional user-provided information, such as the overall weightof a vehicle plus driver and other load, the tire size and type, and theair pressure in tire. In some embodiments, one or more items ofuser-provided information may instead be automatically determined basedon sensor input, such as strain gauge force sensors for weight and tirepressure sensors.

The sensors include one or more pressure transducers 145, configured tomeasure the differential pressure between two sources. In someembodiments, two pressure transducers are used to cooperatively measurewind speed and wind yaw angle directly, in the moving frame of referenceof the object. Particular configurations of the pressure transducers andassociated wind sensor are described below.

The sensors include a direct force power measurement sensor 150, such asa strain gauge operatively coupled to the bicycle pedals, crank, wheelhub, or chain, for measuring power input to the vehicle. The powermeasurement sensor may measure instantaneous and/or average forceapplied to drive the vehicle.

In the case of a human-powered vehicle, the sensors may include acadence sensor 155 for determining pedaling rotational speed. In someembodiments, the cadence sensor may be omitted. In one embodiment,cadence may be estimated from periodic components of signals provided bythe direct force power measurement sensor 150. A Fourier transformanalysis (e.g. fast Fourier transform) of the power measurements may beused to detect the frequency of periodic components corresponding to thecadence. Ground speed measurements may also be used to assist indetermining cadence, for example to discern between the cadencefrequency and higher-order harmonic frequencies in the powermeasurements as expressed in the frequency domain.

The sensors include a speed sensor 160 for measuring speed relative to agiven, typically fixed, reference frame (e.g. ground speed). In someembodiments, the speed sensor includes a Global Positioning System (GPS)unit. In other embodiments, the speed sensor includes a wheel revolutionsensor (e.g., a rare earth magnet coupled to a hall-effect sensor) whichis calibrated with the outer circumference of the wheel. Speed, positionand acceleration can be estimated based on one another using numericaldifferentiation or integration techniques. In one such embodiment, thewheel revolution sensor resolution is improved by affixing multiple rareearth magnets at equally spaced points about the wheel circumference.

The microprocessor 110 operatively coupled to memory 112 (or otherprocessing circuitry) is configured to receive signals from the varioussensors, for example via an intermediate analog-to-digital converters,sampling circuitry, data bus and/or similar components where necessary.The microprocessor, by executing program instructions stored in thememory, performs calculations such as those related to drag estimation,and sends data to the interface device 115 for presentation to a user.

The interface device 115 may include radio frequency communication unitsuch as a Bluetooth™ transceiver configured to wirelessly transmitsignals to another device such as a computer, handheld device such as acell phone, or the like. The interface device 115 may also receive userinput for interacting with the apparatus, for example to configure theapparatus, request stored data records, set user preferences, or thelike. In some embodiments, the interface device may include a displaysuch as an LCD screen and user inputs such as buttons, a touchscreen, orthe like.

The apparatus further includes a power supply such as a lithium ionbattery, along with associated power supply electronics, on/off switch,and the like. The apparatus further includes a housing, such asillustrated below.

FIGS. 3A to 3F illustrate various views of the apparatus according to anembodiment of the present invention. FIGS. 3A to 3D illustratetransparent views of the apparatus including the housing and enclosedcircuitry. FIGS. 3D and 3E illustrate top and front views of thehousing, respectively. FIG. 3F illustrates a close up view of the frontportion of the apparatus, including the 3-hole pitot probe apparatus.

Operation Details

A description of how the sensor data may be used and processed in someembodiments is now provided. In various embodiments, and again in thecontext of a bicycle or ground vehicle, the apparatus may be used toprovide a detailed (and possibly substantially full) characterization ofthe driver's or rider's state, for example including: road slope, objectspeed with respect to ground or another fixed reference frame, objectacceleration, air density, wind speed, wind direction, windacceleration, input power, rolling resistance, rolling resistancecoefficient (C_(rr)), drivetrain and wheel bearing losses, tirepressure, and the history of these state variables in time.

Embodiments of the present invention provide an output variableindicative of rider (or object) coefficient of drag area (C_(D)A) andits variation in time.

Embodiments of the present invention provide an output variableindicative of power being utilized to overcome or undergo one or moreof: air drag; drivetrain losses; rolling friction; rider or objectacceleration (e.g., effects of changes in stored kinetic energy);rotating spoke drag; rider or object changes in elevation/road slope(e.g., effects of changes in potential energy), and wheel rotationalinertia (e.g., effects of changes in stored rotational kinetic energy).

Embodiments of the present invention provide an output variableindicative of wind speed, wind yaw/direction, and wind bursts/gusts(e.g., wind acceleration).

Embodiments of the present invention provide an output variableindicative of metabolic functions, for example used in conjunction withuser inputted data based on a fitness test, such as VO2 max, sweat rate,and lactate threshold data. The metabolic functions may include athletefluid intake requirements, based on a functional relationship withhumidity, air temperature, and heart rate. The metabolic functions mayinclude electrolyte intake requirements. The metabolic functions mayinclude caloric intake requirements.

A first drag computation scenario is now presented. FIG. 4 illustrates ablock diagram showing an object 400 such as a top view of a vehicleequipped with a power meter which measures input power P_(meas) 410 fordriving the vehicle forward variable, a speed sensor measuring groundvelocity U_(rider) 420, and an incoming flow speed sensor which measuresair resistance U_(rel) 430. The measured air resistance includesmagnitude and direction and can be resolved into components U_(rel,x) inthe object main direction of motion (x-direction) 432 and U_(rel,y) 434perpendicular to the object main direction of motion (y-direction).U_(wind) is a vector representation of wind speed (relative to a fixedreference frame), while U_(rel) is a vector representation of the airresistance in the moving reference frame of the object. Thus, U_(rel)can generally be viewed as a vector sum of—U_(wind)+U_(rider).

A first computation operation corresponds to realization of theequation:{right arrow over (U ₀)}=(−|{right arrow over (U)} _(wind)| cos θ+U_(rider)){right arrow over (i)}+(−|{right arrow over (U)} _(wind)| sinθ){right arrow over (j)}   (1)where,U _(rel,x) =−|{right arrow over (U)} _(wind)| cos θ+U _(rider)

In an idealized case, including moving horizontally (for example on aflat road) at a constant speed with no losses and ignoring wheelrotational kinetic energy, further computation operations may correspondto realization of the equations:F _(drag)=½C _(D) Aρ(−|{right arrow over (U)} _(wind)| cos θ+U_(rider))² U _(rider)  (2)P _(meas)=½C _(D) Aρ(−|{right arrow over (U)} _(wind)| cos θ+U_(rider))² U _(rider)  (3)

Here, ρ is the density of the air, {right arrow over (U)}_(wind) is themeasured wind speed in the absolute frame of reference (i.e., from afixed observer), {right arrow over (U)}_(rider) is the ground speed ofthe vehicle, θ is the wind yaw angle in the absolute frame of reference,C_(D)A is the coefficient of drag (C_(D)) of the object/vehicle(typically established from wind tunnel testing) multiplied by thefrontal area (A) of the object/vehicle measured in the y-z plane, i.e.in the plane perpendicular to forward direction of motion. Frontal areamay be estimated for example based on photographs, scaled 3D renderingsof the vehicle, or onboard sensors which detect the human body position.

Embodiments of the present invention are configured, via computationbased on sensor measurements, to estimate the quantity C_(D)A. Thisquantity, for an arbitrary object/vehicle of unknown shape and unknowndrag coefficient, can be computed directly by re-arranging Equation (3)for power:

$\begin{matrix}{{C_{D}A} = \frac{P_{meas}}{{\rho\left( {{{- {{\overset{\rightarrow}{U}}_{wind}}}\cos\mspace{11mu}\theta} + U_{rider}} \right)}^{2}U_{rider}}} & (4)\end{matrix}$

In the presently described embodiment, P_(meas) is obtained from anon-board power meter, ρ is obtained through an established (generallyaccepted) mathematical correlation between temperature, elevation, andrelative humidity. In particular, the density of pure air is computedfrom the ideal gas law, ρ=P/R_(a)T, where P is the static (absolute)pressure, T is the absolute temperature, and R_(a) is a specific gasconstant for dry air. The addition of water vapour into the air isaccounted for by computing the mixture of two ideal gases with thefollowing equation:

$\begin{matrix}{\rho_{{humid}\mspace{14mu}{air}} = {\frac{P_{a}}{R_{a}T} + \frac{P_{v}}{R_{v}T}}} & (5)\end{matrix}$where ρ_(humid air) is the density of the humid air, P_(a) is thepartial pressure of dry air, R_(a) is the specific gas constant for dryair, P_(v) is the partial pressure of water vapour, and R_(v) is thespecific gas constant for water vapour. The partial pressure of the dryair can be computed according to:P _(a) =P−P _(v)  (6)where P is the observed or measured absolute pressure, and P_(v) iscomputed using the measured relative humidity as follows:

$\begin{matrix}{P_{v} = {\gamma\left( {{0.0}61078 \times 10^{\frac{7.5T}{T + 237.3}}} \right)}} & (7)\end{matrix}$where γ is the relative humidity. {right arrow over (U₀)}, {right arrowover (U)}_(wind), as well as θ, are obtained directly from the windsensor (e.g. 3-hole pitot probe) and from the ground speed obtained viathe (ground) speed sensor.

A second drag computation scenario is now presented. This scenario isapplicable for a vehicle which is climbing (gaining altitude) andaccelerating. FIG. 5 illustrates a block diagram showing an object 500such as a side view of a vehicle equipped with a power meter whichmeasures input power P_(meas) for driving the vehicle forward variable,a speed sensor measuring ground velocity U_(rider) 520, and an incomingflow speed sensor which measures air resistance U_(rel). The climbing(inclination) angle α 540 is also shown.

For the sake of clarity, it is assumed that the weight of the vehicleplus its driver/rider is included or added to calibration data, W_(rb)550. The rider or object is equipped with a gyroscope device to measurethe (e.g. instantaneous) inclination angle α, as well as anaccelerometer device to measure (e.g. forward) acceleration. Inclinationangle can correspond to the angle, relative to the direction of gravity,of the ground surface at the location of the vehicle. The sum of forcesacting on the rider becomes more complex than in the first scenario,with the addition of gravitational force as well as relativeacceleration.

Neglecting frictional losses, the acting forces can be expressed as:ΣF _(x) =F _(drag) +W _(rb) sin α=m _(rb) a _(rel)  (8)where m_(rb) is the mass of the object (e.g. bike+rider), computed asm_(rb)=W_(rb)/g, where g is the local acceleration due to gravity, anda_(rel) is the resultant acceleration of the rider in the x-direction,measured directly using an accelerometer and/or other suitable sensor(e.g., through numerical differentiation of velocity measurements).

Rearranging the above for C_(D)A yields:

$\begin{matrix}{{C_{D}A} = \frac{\begin{matrix}{P_{meas} - {W_{rb}\sin\mspace{11mu}{\alpha\left( {{{- {{\overset{\rightarrow}{U}}_{wind}}}\cos\mspace{11mu}\theta} + U_{rider}} \right)}} +} \\{m_{rb}{a_{rel}\left( {{{- {{\overset{\rightarrow}{U}}_{wind}}}\cos\mspace{11mu}\theta} + U_{rider}} \right)}}\end{matrix}}{{\rho\left( {{{- {{\overset{\rightarrow}{U}}_{wind}}}\cos\mspace{11mu}\theta} + U_{rider}} \right)}^{2}U_{rider}}} & (9)\end{matrix}$

In this second scenario, P_(meas) may be obtained from an on-board powermeter, ρ may be obtained through an established (generally accepted)mathematical correlation between temperature, elevation, and relativehumidity and {right arrow over (U₀)}, {right arrow over (U)}_(wind), aswell as θ, may be obtained directly from the wind sensor (e.g. 3-holepitot probe) and the ground speed obtained via the (ground) speedsensor.

In various embodiments, frictional losses may be incorporated into thecomputations. The second scenario above illustrates the basicfunctionality according to an embodiment of the present invention.Additional sensors may be provided and utilized in order to compensatefor frictional losses associated to the vehicle drivetrain as well asrolling friction. For both of these types of losses, the empirical modelemployed by Martin et al. (1998)—“Validation of a mathematical model forroad cycling power” J. App. BioMech, Vol. 14(3) and Martin et al.(2006b)—“Aerodynamic drag area of cyclists with field-based measures”,Sportscience 10: 68-9 may be used, both of which are hereby incorporatedby reference. What is used in these models is the coefficient of rollingresistance, which may be determined for example via a calibrationprocedure, as well as the current cadence, which may be obtained via anonboard cadence sensor. Alternative mathematical or empirical models offrictional losses may also be incorporated depending on the locationwhereby the power measurement is being completed (e.g., a power sensorlocated on a crankshaft would contain different losses than a powersensor located in a wheel hub).

In contrast to other methods, such as work by Snyder &Schmidt—“Determination of Drag Parameters Utilizing a Bicycle PowerMeter,” Human Powered eJournal, Article 05, issue 01, (Oct. 21, 2004)and available at http://www.hupi.org/HPeJ/0005/0005.htm and herebyincorporated by reference, embodiments of the present invention do notnecessarily require controlled conditions, such as the imposition ofzero acceleration effects, and zero wind effect, for an adequateaerodynamic analysis.

Computations for evaluating one or more of the above equations may beperformed by the processing circuitry (e.g. microprocessor operativelycoupled to memory). For example, computations for evaluating Equations(4) or (9), or similar equations can be performed. In some embodiments,computations are performed by the microprocessor using standardfloating-point methods. In some embodiments, the computations areapproximated using a lookup table method, in which the solutions to oneor more equations are pre-computed for various combinations of inputvariables and stored in memory. Sensor input (potentially along withcalibration data indicating values for input variables or parameterswhich are not sensed) is used as input to a lookup operation to retrievea stored solution which is appropriate for the present set of inputvalues, including sensor input. In some embodiments, when a storedsolution is not available for a given set of input values, interpolationor extrapolation may be performed in order to obtain an approximatesolution. In some embodiment, digital or analog processing circuitry canbe configured to automatically receive and process input signals fromsensors to provide output signals which are based on the input signalsin a predetermined manner which implements the computations describedabove.

Sensor Detail: Wind Sensor

Embodiments of the present invention provide an air flow speed anddirection sensor, also referred to as a wind sensor. The term “wind” mayrefer to the motion of any fluid relative to a moving object, which maybe due to one or both of the object's motion and the fluid motion.

For an object inserted into a flowing fluid, such as air, the pressuredistribution over the surface of the body varies from a maximum(stagnation pressure) to minimum values which can be lower than thestatic pressure of the fluid (absolute pressure). The stagnationpressure is calculated as the sum of the static and dynamic pressures:P _(stag) =P _(∞) +ρU _(o) ²  (10)

The main purpose of a multi-hole pitot probe is to measure the localpressure at different points on the curved surface of an object in orderto discern the direction and magnitude of the incoming flow speed.Multi-hole probes can be calibrated analytically or experimentally,though the latter is more often employed.

FIG. 6 illustrates an apparatus comprising pressure transducers 625, 627used as a wind speed and yaw angle sensor, according to an embodiment ofthe present invention.

A housing 610 is provided having at least three forward-facing pitottubes 620 which are each open at one end. The openings correspond topressure ports 1, 2, 3. The pressure transducers 625, 627 are coupled atinterior locations of the pitot tubes 620 for measuring stagnationpressure. The direction of the incoming flow is identified in FIG. 6using streamlines and arrows. As illustrated, a first pressuretransducer 625 is coupled to both a first pitot tube connected to acentral one of the pressure ports 1, and a second pitot tube connectedto a pressure port 2 located on one side of the central pressure port 1.A second pressure transducer 627 is coupled to both the first pitot tubeconnected to the central one of the pressure ports 1, and a third pitottube connected to a pressure port 3 located on another side of thecentral pressure port 1. The pitot tube connecting the central pressureport 1 to the two pressure transducers is a split pilot tube, that ishaving a “Y” shape and three endpoints.

Analytical Solution:

Assuming the flow development around the probe is approximated as thepotential flow around a cylinder with circular cross section, ananalytical potential flow solution can be used to quantify the velocityon the cylinder as:V(θ)=2V sin β  (11)where θ is the angular distance from the point of stagnation to thepoint of interest (FIG. 6). Bernoulli's equation can then be employed tocalculate the pressure at the three pressure taps as shown below:P _(∞)+½ρU _(o) ² =P(δ−θ)+2ρU _(o) ² sin²(δ−θ)  (12)P _(∞)+½ρU _(o) ² =P(θ)+2ρU _(o) ² sin²(θ)  (13)P _(∞)+½ρU _(o) ² =P(δ+θ)+2ρU _(o) ² sin²(δ+θ)  (14)

The three equations (12) to (14) can be utilized as follows: if thepressure at ports 1, 2, and 3 are measured, then the system of equations(12) to (14) can be solved for the unknowns P_(∞), U_(o), θ, whereinP_(∞) represents the local value of the static pressure, U_(o)represents the local speed of the incoming flow relative to the probe,and θ represents the yaw angle of the flow relative to the probe.

However, the location of the pressure taps are subject to manufacturingconstraints, which introduces measurement errors. In particular,manufacturing tolerances for both the pressure tap hole size and holeposition will result in variances in the resulting pressuremeasurements, introducing measurement (bias) errors. The measurementerrors can be corrected for through experimental calibration, forexample as discussed below.

Experimental Calibration:

Experimental calibration can be completed by inserting the probe into aknown flow field (e.g., a wind tunnel facility), traversing various yawangles, and measuring the corresponding pressures. This type ofexperimental calibration is optional according to embodiments of thepresent invention. The formulas and discussion here pertain tothree-hole probes, but extensions to any number of holes isstraightforward and can be found in the literature (e.g., Johansen, E.S., Rediniotis, O. K., Jones, G., “The compressible calibration ofminiature multi-hole probes”, Journal of Fluids Engineering 123, pp.128-138, 2001). The calibration can be done by the ‘StreamlineProjection Method’, which is based on the assumption that the freestream velocity is projected on each one of the three sensing holes(pressure ports) 1, 2, 3. Therefore, the velocity normal to the probesurface results in a dynamic pressure, which is added to the free streamstatic pressure. Thus, the holes of the probe are assumed to measure atotal pressure which is equal to the static pressure plus the fractionof the dynamic pressure based on the velocity projection normal to eachof the holes. This can be expressed via the equation:P _(i) =P _(∞)+½ρw _(i) ²  (15)where i=1, 2, 3, corresponds to holes/ports 1, 2, 3, as in FIG. 6, andw_(i) is the velocity projection normal to the i^(th) hole.

The first step is to obtain the three flow velocity components normal tothe hole surfaces, expressed as:w ₁ =U _(o) cos θ  (16)w ₂ =U _(o) cos(β+θ)  (17)w ₃ =U _(o) cos(β−θ)  (18)

The three holes thus sense the following pressures:P ₁ =P _(∞)+½ρ(U _(o) cos θ)²  (19)P ₂ =P _(∞)+½ρ(U _(o) cos(β+θ))²  (20)P ₃ =P _(∞)+½ρ(U _(o) cos(β−θ))²  (21)

Next, coefficients are defined pertaining to the experimentalcalibration:

An average pressure coefficient is defined as:

$\begin{matrix}{\overset{\_}{P} = \frac{P_{2} + P_{3}}{2}} & (22)\end{matrix}$

A directional coefficient is defined as:

$\begin{matrix}{k_{\theta} = {\frac{P_{3} - P_{2}}{P_{1} - \overset{\_}{P}} = \frac{k_{3} - k_{2}}{k_{1} - \overset{\_}{k}}}} & (23)\end{matrix}$

The wind yaw angle is estimated directly from the directionalcoefficient via the equation below:

$\begin{matrix}{\theta = {{\sin^{- 1}\left( \frac{k_{\theta}}{6} \right)} \times \frac{180}{\pi}}} & (24)\end{matrix}$

The incoming wind speed is estimated directly from the average pressureas well as an experimentally determined calibration coefficient with theequations below:

$\begin{matrix}{C = \frac{U_{o,{calibration}}}{\sqrt{\frac{2\left( {P_{1} - \overset{\_}{P}} \right)}{\rho}}}} & (25) \\{U_{o} = {C \times \sqrt{\frac{2\left( {P_{1} - \overset{\_}{P}} \right)}{\rho}}}} & (26)\end{matrix}$

In Equation (25) above, U_(o,calibration) is the primary parameter beingcontrolled in the wind tunnel (i.e., the free stream of the wind tunnelis set), and the corresponding coefficient C is obtained as an ensembleaverage of several tests over a wide range of flow speeds and wind yawangles. This coefficient (C) is stored in memory for application in areal environment.

The use of a three-hold probe for estimation of the free stream velocityand wind yaw angle is acceptable for yaw angles less than about 15°.(For larger wind yaw angles, such as yaw angles up to about 30°, afive-hole probe may be selected.) Specific calibration experiments wereperformed using a prototype device in a wind tunnel. The experimentsrevealed that the above method resulted in estimates of free streamvelocity and yaw angle which were within 2% of their true values, with95% confidence.

Dynamic Calibration in a Real Environment:

The above-mentioned experimental calibration is typically performed in awind tunnel facility where no physical obstructions are altering theflow path or pressure field around the probe (aside from the probeitself). It can be expected that in a given engineering application, thepitot probe calibration would need to be corrected to account for nearbywall or interference effects. In the case of a pitot probe mounted to abicycle, the rider and bicycle are anticipated to affect the surroundingpressure field, including regions upstream of the probe itself. Hence,the following procedure is outlined whereby the calibration data for thepitot probe is dynamically generated and/or altered based on theposition of the rider and bicycle relative to the position of the probe(as discussed above the rider and bicycle may be replaced with anyvehicle or object to which the probe is mounted). Generally, thecalibration procedure may be carried out based on the presence of anobject which is partially or fully downstream of the probe (i.e. on thelee side with respect to air motion relative to the object) but whichnevertheless affects air flow as measured by the probe. If the object ispartially upstream of the probe, it should be in a location which is notdirectly in front of the probe and/or which does not cause the object tointerfere with the fluid approaching the probe.

The dynamic in situ calibration is performed following attachment of thesensor to an object. In some embodiments, the sensor is pre-calibratedunder controlled conditions such as in a wind tunnel, and thenre-calibrated following mounting to the object. The re-calibration maycompletely overwrite the pre-calibration in some embodiments. In someembodiments, the pre-calibration step is omitted.

Because the fundamental equations derived for estimating the flowvelocity and wind yaw angle follow the assumption of a potential flowfield, the same assumption is applied for the bike and rider. Thisenables the principle of superposition to be applied. Specifically, theflow field solution for the probe itself can be superimposed on the flowfield solution for the bike plus the rider in order to adjust thecalibration. The level of sophistication in the potential flow model mayvary depending on the number of sensors employed. For the purposes ofclarity and illustration, in the present example, a single infraredproximity sensor is used to measure the position of the rider relativeto the probe itself (or it is information inputted by the user), and theprobe is installed in a known location relative to the bicycle (Δx). Inthis example, the bike plus the rider is approximated as a rankinehalf-body whose forward stagnation point is positioned based on userinput or the infrared sensor measurement, as shown in FIG. 7. In someembodiments, the body (e.g. the bike plus rider) may be approximatedusing a different shape or model, other than the rankine half-body. Theshape or model to be used may be based on theoretical reasoning and/orexperimental testing, for example.

As shown in FIG. 7, the position of the probe relative to the rankinehalf-body is given by a streamwise distance Δx, wherein the airflowdirection is aligned with the symmetry plane of the rankine body,facilitating the computation of the pressure field and velocity fieldinduced by the presence of the body.

The basic governing equation of the streamfunction (based on thecoordinate axis provided in the FIG. 7) is given by:

$\begin{matrix}{\Psi = {{U_{\infty}y} + {m\;{\tan^{- 1}\left( \frac{y}{x} \right)}}}} & (27) \\{m = \frac{y_{v}U_{o}}{\pi}} & (28)\end{matrix}$where y_(v) is the half-width of the vehicle (e.g., half-width of therider). The velocity of the flow at any position in front of the vehiclewill be less than that of the free stream velocity, U_(∞), as given bythe following equations:

$\begin{matrix}{{u = \frac{\partial\Psi}{\partial y}};{v = \frac{\partial\Psi}{\partial x}}} & (29) \\{{U\left( {x,y} \right)} = \sqrt{u^{2} + v^{2}}} & (30)\end{matrix}$

In polar coordinates the equations are more amendable to analyticalsolution, yielding:

$\begin{matrix}{V_{r} = {{{U_{o}\cos\;\phi} + \frac{m}{r}} = {{{- U_{o}} + \frac{m}{{\Delta\; x} + a}} = {{- U_{o}} + \frac{y_{v}U_{o}}{\left( {{{\pi\Delta}\; x} + y_{v}} \right)}}}}} & (31) \\{\left. V_{Ø} \right.\sim 0} & (32)\end{matrix}$

Superimposing the solution to the rankine body with the three-holeprobe, the free stream velocity magnitude is expected, as seen by thepitot tube, to decrease by approximately:

$\begin{matrix}{{\Delta\; U} = \frac{y_{v}U_{o}}{\left( {{{\pi\Delta}\; x} + y_{v}} \right)}} & (33)\end{matrix}$

That is, ΔU represents the difference between the true value of U_(o)and the measurement V_(r). This quantity can be used in measurementcorrection.

In this formulation, no correction is applied for the change in windvelocity in the tangential direction, as it is assumed the pitot probeis mounted symmetrically relative to the downstream body (bike+rider).As an example, when travelling at

${U_{o} = {{1{0\left\lbrack \frac{m}{s} \right\rbrack}} = {3{6\left\lbrack \frac{km}{h} \right\rbrack}}}},$with zero wind yaw, and assuming a pitot probe position of Δx=0.5 [m],and for a rider with y_(v)=0.2 [m], the locally measured air speed willbe altered by approximately:

$\begin{matrix}{{\Delta U} = {\frac{y_{\nu}U_{o}}{\left( {{\pi\Delta x} + y_{\nu}} \right)} = {\frac{\left( {0.2} \right)\left( {10} \right)}{\left( {{{0.5}\pi} + 0.2} \right)} = {{1.1}{2\left\lbrack \frac{m}{s} \right\rbrack}}}}} & (34)\end{matrix}$

As shown in Equations (33) and (34), the presence of a body behind apitot probe (e.g., a rankine half-body) impacts the performance of theprobe by introducing errors on the order of 10% of the free streamvelocity. The dynamic calibration involves correcting the magnitude ofthe velocity as measured by the pitot tube using the above equation,with direct input from an infrared proximity sensor providing sensorvalue Δx. In this configuration, the measured local yaw angle of thewind is assumed to be unaffected within the designed measurement rangeof the 3 hole probe, i.e., −15°≤θ≤15° (though it is contemplated that analternative approach is to compute a streamfunction for another knownyaw angle and include its effects). For higher angles of attack, a moresophisticated streamfunction can be developed for the downstream body(e.g., bike plus rider).

The implementation of a dynamically changing streamfunction forcalibration adjustments to the upstream pitot tube is applicable for avariety of dynamic environments in which the shape of the downstreambody is deformable (e.g., physically movable like a human on a bicycle),or the shape of the body is a function of yaw angle.

Experimentally Determined Dynamic Calibration from Field Based Measures:

An alternative calibration adjustment to the pitot probe can becompleted via field based measures (or wind-tunnel based measures) ofthe downstream body by following the protocol described next.

First, the device prompts the user for a calibration of the pitot tubeonce activated and all sensors are communicating.

Next, the device prompts the user for the number N of physicalconfigurations of the body to be calibrated.

Next, for each physical configuration, indexed by i=1:N, the deviceprompts the user to bring the device up to cruising speed in physicalconfiguration i under a condition of zero external wind (i.e.substantially no air motion relative to ground). The device then promptsthe user to stop calibration i.

In more detail, upon receipt of the number N, the device stores intomemory the number of physical configurations for the body (bike+rider),and enters a loop to obtain calibration coefficients for each of theaforementioned positions.

Following the prompt to bring the device to cruising speed for a givenconfiguration i, the device will measure and store infrared sensor data(or other data indicative of body position in proximity to the probe)for physical configuration i, while simultaneously storing pressure dataand ground speed data. The average infrared sensor reading and standarddeviation of that reading will be used to create a calibration range forconfiguration i. The pressure data will be corrected for the groundspeed by generating a streamfunction which facilitates the correction inthe measured velocity, as given in Equation (33) above, for example.

Following a prompt to stop a given calibration, the calibration data isstored into memory, and the process is repeated for all physicalconfigurations.

This procedure enables the calibration for the pitot tube sensor to bedynamically changing depending on the infrared sensor reading. Theinfrared sensor reading can be readily replaced by a number of sensorswhich establish distinct physical configurations of the downstream body.Additionally, the infrared sensor can be replaced by dynamic user ormachine input to indicate a change in physical configuration.

In various embodiments, the above calibration protocols can be used toyield a set of N wind sensor correction factors (or other calibrationparameters) associated with N physical object configurations (e.g. riderpositions). The N object configurations are also associated with Ndifferent proximity sensor reading ranges. Subsequently, duringoperation, output of the proximity sensor is used to select which windsensor correction factor is to be applied. Specifically, when theproximity sensor readings fall within a range which is associated withone of the N object configurations, the corresponding wind sensorcorrection factor is retrieved from memory and applied.

Configuration of 3-Hole Probe Pressure Transducers:

When a 3-hole probe is utilized, the expectation is that three distinctpressure measurements are used in order to obtain estimates of the windspeed and wind yaw angle based on the equations (22)-(26) outlined inthe above sections.

These equations are repeated here for clarity for the experimentalcalibration:

Average Pressure:

$\begin{matrix}{\overset{\_}{P} = \frac{P_{2} + P_{3}}{2}} & (22)\end{matrix}$

Directional Coefficient:

$\begin{matrix}{k_{\theta} = {\frac{P_{3} - P_{2}}{P_{1} - \overset{\_}{P}} = \frac{k_{3} - k_{2}}{k_{1} - \overset{\_}{k}}}} & (23)\end{matrix}$

The wind yaw angle is estimated directly from the directionalcoefficient:

$\begin{matrix}{\theta = {{\sin^{- 1}\left( \frac{k_{\theta}}{6} \right)} \times \frac{180}{\pi}}} & (24)\end{matrix}$

The incoming wind speed is estimated directly from the average pressureas well as an experimentally determined calibration coefficient:

$\begin{matrix}{C = \frac{U_{o,{calibration}}}{\sqrt{\frac{2\left( {P_{1} - \overset{\_}{P}} \right)}{\rho}}}} & (25) \\{U_{o} = {C \times \sqrt{\frac{2\left( {P_{1} - \overset{\_}{P}} \right)}{\rho}}}} & (26)\end{matrix}$

As shown in the above equations, relevant quantities usable forestimating wind yaw and wind speed are (P₃−P₂), and (P₁−P). Using adifferential pressure transducer on the 3-hole probe, it is possible tomeasure the difference between P₃ and P₁. A second probe can be used tomeasure the difference between P₂ and P₁:ΔP ₁₃ =P ₁ −P ₃  (35)ΔP ₁₂ =P ₁ −P ₂  (36)

The above measurement can be summed or subtracted to provide importantpressure quantities for flow speed and airflow yaw angle calculation:ΔP ₁₂ −ΔP ₁₃=(P ₃ −P ₂)  (37)½(ΔP ₁₂ +ΔP ₁₃)=P ₁−½(P ₂ +P ₃)=(P ₁ −P )  (38)

Embodiments of the present invention therefore provide a pitot-probewind sensor having two differential pressure transducers configured asdescribed above. For alternative configurations, individual pressuresare measured relative to the absolute or static pressure.

The above configuration of two differential pressure transducers allowsfor adequate sensor functionality with a reduced number of components,for example with two rather than three pressure transducers employed.The two pressure transducers are differential pressure transducers. Afirst one of the two differential pressure transducers is coupled tofirst and second pitot tubes for measuring differential pressure. Asecond one of the two differential pressure transducers is coupled tothe first pitot tube and a third pitot tube for measuring differentialpressure. In various embodiments, the first pitot tube has a pressureport opening located between port openings of the second and third pilottubes. That is, the first pilot tube is a central, forward facing pilottube whereas portions of the second and third pitot tubes facediagonally forward and outward at opposite sides of the first pitottube. The first pitot tube may include a fork or “Y” junction forcoupling the pressure port thereof to both pressure transducers. Acomputing component, such as processing circuitry (e.g. amicroprocessor), is operatively coupled (potentially via ananalog-to-digital converter and other intermediate components) to thefirst and second pressure transducers for obtaining readings therefrom.The computing component provides further data based on the measurementsfrom the transducers, for example as set forth in Equations (37) and(38).

In various embodiments the pitot tubes are curved such that portions ofthe tubes proximate to the pressure ports face outward in threedifferent directions, for example forward and diagonally forwarddirections, and ends of the tubes proximate to the pressure sensors arelocated relatively so as to allow differential pressure readings to beobtained between pairs of tubes.

Sensor Detail: Road Surface Sensor

Embodiments of the present invention provide for a road surface sensorwhich is configured, based on measured vibrations, to determine a typeof surface being traversed by a vehicle such as a bicycle, and/or acoefficient of rolling resistance which varies based on the type ofsurface. The surface may be, for example, smooth asphalt, rough asphalt,gravel, dirt, or another type of surface. Vibrations may be measuredusing a piezoelectric transducer, for example.

As outlined by Martin et al. (1998)—“Validation of a mathematical modelfor road cycling power” J. App. BioMcch, Vol. 14(3) (hereinafter Martin(1998)), the force on a wheeled object due to rolling resistance isrelated to the weight of the object (e.g. the weight of a bike andrider), the tire pressure, tire material, wheel type (casing), andgradient and texture of the riding surface. All of these effects aregrouped together in what is commonly referred to as a coefficient ofrolling resistance, or C_(RR). The force due to rolling resistance(F_(RR)) is given by Martin (1998) as:F _(RR) =C _(RR) W _(rb) cos α  (39)

Note that the weight W_(rb) of the object (e.g. bike+rider) isuser-inputted, while the road slope is measured experimentally, givingangle α in Equation (39). The aspects of the rolling resistance force tobe accounted for are the effects of tire pressure, tire type, andtexture of the riding surface, all of which will impact the coefficientof rolling resistance.

In “The mechanics and aerodynamics of cycling,” Kyle, C. R., E. R. Burke(Ed.), Medical and Scientific Aspects of Cycling, pp. 235-251,Champaign, Ill.: Human Kinetics, (1988), C_(RR) values ranging from0.0027 to 0.0040 for clincher bicycle tires are reported. These rollingresistance values were determined using controlled experimental testingon smooth asphalt (Kyle, 1988). In embodiments of the present invention,a baseline coefficient of rolling resistance is determinedexperimentally. A basic model is provided which incorporates thecombined effect of tire pressure and road surface condition.

For determining a baseline coefficient of rolling resistanceexperimentally, a coast-down procedure is employed. The generalcoastdown testing procedure outlined by “Road Load Measurement andDynamometer Simulation Using Coastdown Techniques,” J1263, Society ofAutomotive Engineers (SAE), 1996, is employed with minor modificationsthat are pertinent only to the specific engineering application (e.g.,bicycles versus automobiles). In the present invention, the coast-downprocedure is electronically controlled, whereby a user followsstep-by-step instructions and performs a coast-down maneuver. Sensordata acquired during the test is utilized to obtain a measure of thecoefficient of rolling resistance, C_(RR), under the controlledconditions of the test.

In embodiments of the present invention, an additional sensor isutilized to record vibration measurements during the coast-downprocedure. The mean amplitude of the vibration measurements as well asthe variance in the amplitude of the vibration measurements provides acalibration starting point. In particular, the coefficient of rollingresistance is assumed to remain constant on a short time interval, if,in that short time interval, the mean amplitude of the vibrationmeasurement is within one standard deviation of variance computed in thecalibration. If the mean amplitude of the vibration measurement fallsoutside of one standard deviation of the variance computed in thecalibration, then the coefficient of rolling resistance is adjustedusing the following formula (derived empirically through field testing):

$\begin{matrix}{C_{RR} = {C_{{RR},{calibration}}\left( {1 + {C\left\lbrack \frac{{\overset{\_}{a}}_{calibration} - {\overset{\_}{a}}_{meas}}{{\overset{\_}{a}}_{calibration}} \right\rbrack}} \right)}} & (40)\end{matrix}$

In Equation (40), ā is the normalized short time average peak-to-peakamplitude of vibrations, and C is a constant value determined by causingthe processing circuitry to perform a continuous linear regression fitof the vehicle power to overcome drag relative to the power to overcomerolling resistance. It is the y-intercept of this linear fit whichdetermines directly an estimate of the coefficient of rolling resistanceand hence, enables computation of parameter C. This procedure can besuperseded by a basic linear equation if multiple coast-down tests areperformed under different road surface conditions and tire pressures. Itis noted that empirical real-time computation of coefficient of rollingresistance and the constant C may be data which are stored in memory forfuture use under similar conditions.

Additional Drag Component

In some embodiments of the present invention, an additional dragcomponent acting on a moving body can be accounted for, particularlywhen there is an acceleration of fluid around the moving body or viceversa. This additional drag component may be particularly applied whenthe body and/or fluid is aggressively accelerating. Additionally oralternatively, the additional drag component may be applied morefrequently in a water based (highly viscous) fluid environment.

Naturally, when a body is accelerating in a fluid, there is what isknown as an “inertial effect” on the drag due to the mass of the bodyand its acceleration. But, in addition to this inertial force, there isalso a drag component that arises from the fact that work is being doneon the fluid in order to accelerate it around the body. This additionalenergy requirement is known as the “added mass effect”. In fluidmechanics, added mass or virtual mass has been described in variousreferences, for example in Newman, John Nicholas (1977), “Marinehydrodynamics,” Cambridge, Mass.: MIT Press. § 4.13, p. 139. ISBN0-262-14026-8, and https://en.wikipedia.org/wiki/Added_mass.

According to embodiments of the present invention, some equationsregarding added mass are incorporated to improve the accuracy ofmeasurements under cases of large accelerations or decelerations. In oneembodiment, an apparatus may be configured to measure wind speed andground speed simultaneously, and gradient estimations may be used todetermine the acceleration of the fluid around the body. This may inturn be used to estimate the “added mass” force. In nearly all cases inair this force is quite small and may be considered negligible for manyapplications. But, for hydrodynamics applications, the added mass effectbecomes important. The effect may also be important in certain very highprecision aerodynamic applications.

Added mass and history force equations are obtained by adapting theapproach of Odar, F., & Hamilton, W. S. (1964), “Forces on a sphereaccelerating in a viscous fluid,” Journal of Fluid Mechanics, 18(02),302-314:

$\begin{matrix}{F = {{C_{A}{ma}} + {C_{H}L^{2}\sqrt{\pi\rho\mu}{\overset{t}{\int\limits_{0}}{\frac{a\left( t^{\prime} \right)}{\sqrt{t - t^{\prime}}}{dt}^{\prime}}}}}} & (41)\end{matrix}$

They empirically derived their added mass and history forcecoefficients,

$\begin{matrix}{{C_{A} = {{1.05 - {\frac{0.066}{{Ac}^{2} + 0.12}\mspace{14mu}{and}\mspace{14mu} C_{H}}} = {2.88 + \frac{3.12}{\left( {{Ac} + 0.12} \right)^{3}}}}};} & (42)\end{matrix}$

where

${{Ac} = \frac{v^{2}}{ad}},$the ratio of convective acceleration to local acceleration (Odar &Hamilton, 1964), and L is a length scale pertaining to the size of thebody (e.g. bike+rider).

Similar empirical correlations can be obtained experimentally throughwind tunnel testing and employed in the present invention in order toestimate “added mass” effects on the drag coefficient.

Further Details and Uses

Embodiments of the present invention may incorporate or be coupled toone or more actuators. The processing circuitry may transmit controlsignals to the actuators to implement a change based on current sensorreading.

For example, a servo motor and actuator may be actuated based on sensorreadings. As another example, an actuator which is configured to performan energy efficiency pitch change operation or a safety operation suchas a stabilization operation may be provided. The actuator may becontrolled using feedback from the sensor, according to a particularfeedback control approach.

In some embodiments, the apparatus is configured to measure attributessuch as aerodynamic drag, drive train loss, rolling resistance and windspeeds (directions, bursts and gusts) at a given frequency, for example10 times per second, and data can be provided based on such measurementssubstantially immediately. The apparatus may be configured cancommunicate to a user interface directly through a wire or remotely toseveral actuators such as servo motors, safety shutdown controllers,pressure pumps, redirection vents, air flow fins, etc. Communication maybe via Bluetooth™, for example. In some embodiments, control of theactuators may provide for increased fluid-dynamic performance or anotherpurpose.

FIGS. 8A and 8B illustrates test data showing a correlation betweenpower output and drag according to an embodiment of the presentinvention. For this embodiment, a bicycle rider moved from a seatedposition to a standing position and then performed an acceleration. Theresults shown in FIGS. 8A and 8B illustrate that the measured peak poweron each burst is consistently higher than the estimated peak power. Inparticular, the average measured peak power is 994 W compared to anestimated power of 930 W, corresponding to a reduction in power of 7%.In other words, if the rider was to remain in the seated position, thesame performance could be achieved with a reduction in power of 7%. Thisresult provides direct insight into the aerodynamic performance of theburst accelerations. Note, however, it is likely impossible for therider to produce the same power from a seated position when compared tostanding. Nevertheless, it is worthwhile for the rider to consideralternative sprinting positions in order to converge on an optimalcombination of aerodynamics and power production.

FIGS. 9A and 9B illustrates typical variations of four parameters for asmall segment of a controlled ride in an outdoor velodrome, according toan experiment conducted in relation to an embodiment of the presentinvention. The four parameters include: (i) the power to overcome dragforce, (ii) the power to overcome road slope, (iii) the power ofacceleration, and (iv) the power to overcome rolling resistance. Thetotal rider input power can be equated with the sum of all forces actingon the rider, multiplied by the rider ground speed.

For the illustrated small segment, the test rider was instructed to holda constant power of approximately 250 W over 5 laps. The rider beginswith an aggressive acceleration reaching a peak power of about 400 W(red line in FIG. 9A). The sensor data indicates that the power requiredto accelerate the rider peaks at slightly under 300 W (green line inFIG. 9A). When combined with the power to overcome drag (black line inFIG. 9A) and the rolling resistance (blue line in FIG. 9A), theestimated rider power is well predicted. Following the initialacceleration, the rider stabilizes his input power at roughly 250 W.Over the course of the 5 laps (t=0.25 to 3.5 in FIGS. 9A and 9B), boththe measured input power and estimated input power fluctuate slightly,but for different reasons. The measured power is fluctuating as theriders power transfer from his legs, through into the pedals will beimpossible to keep perfectly constant. On the other hand, the estimatedpower fluctuates due to changes in the sensor measurements andassociated estimates of power, particularly changes in relative windspeed (FIG. 9B) and small changes in the rider's acceleration (FIG. 9A).Overall, the average power and RMS power during the quasi-steadyinterval between t=0.25 min and t=3.5 min is: P(measured)=248.62 W;P(estimated)=249.10 W; P_(RMS)(measured)=11.21 W; andP_(RMS)(estimated)=19.73 W.

The results indicate that on the average, the experimental embodimentcould be used to accurately measure the riders input power undercontrolled conditions. This also suggests that the sensor measurementsbeing provided have a reasonable accuracy. Using these sensor readings,a calibration has been established for the rider. When the rider choosesa different body position, his fluid-dynamic performance under varyingconditions can be compared with this calibration.

FIG. 10 illustrates a method for determining fluid dynamic drag on anobject, in accordance with an embodiment of the present invention. Themethod includes obtaining 1010 sensor readings from one or a combinationof sensors, the sensor readings indicative of external thrust forces orresistive forces applied to the object. The method includes determining1020 using a computer, a coefficient of drag area based on the sensorreadings and optionally one or more stored parameters, according to apredetermined relationship.

FIG. 11 illustrates a method for calibrating a multi-hole pitot probewind sensor, in accordance with an embodiment of the present invention.The method includes receiving 1110 an indication of a body proximate tothe probe; estimating 1120 a flow field induced by the presence of thebody at least in the vicinity of the probe; performing 1130 computationsrelated to a superposition of the estimated flow field onto another flowfield for the probe; estimating 1140 a measurement error induced in theprobe by the body, the estimate based on the superposition; andproviding 1150 a correction factor for at least partially countering themeasurement error.

FIG. 12 illustrates a method for calibrating a multi-hole pitot probewind sensor, in accordance with another embodiment of the presentinvention. The method includes providing 1210 a set of one or moreconfigurations for a body proximate to the probe; and for each of theset of configurations, experimentally determining 1220 a measurementerror induced in the probe by the body and providing 1230 a correctionfactor for at least partially countering the measurement error.

FIG. 13 illustrates a method for operating a multi-hole pitot probe windsensor, in accordance with an embodiment of the present invention. Themethod includes receiving 1310 an indication of relative location and/orshape of a body proximate to the probe; and providing 1320 a correctionfactor to be applied to measurements from the probe based on thereceived indication.

FIG. 14 illustrates a method for determining rolling resistance exertedby a surface on a wheeled object, in accordance with an embodiment ofthe present invention. The method includes measuring 1410, using avibration sensor, vibrations due to rolling of the wheeled object on thesurface; and determining 1420, using a computer, a coefficient ofrolling resistance based on the measured vibrations and one or morestored parameters, according to a predetermined relationship.

Embodiments of the present invention may be applied in the field ofconsumer sports equipment. For example, the apparatus may be configuredas a cycling computer or monitor for use by a person or a human-poweredvehicle.

Embodiments of the present invention may be applied in thetransportation field. For example, trucking companies may incorporatethe apparatus on transportation trucks to monitor vehicle efficiency,for example incorporating fluid-dynamic analysis. In one embodiment, theapparatus is integrated into other systems on the truck such as trucktire inflating systems, which are presently manually adjusted by thedriver. The present invention may be configured for mitigating issuessuch as tire wear, managing tire safety pressures for both highwayblowouts and providing better traction in certain road conditions suchas on mountain passes.

Embodiments of the present invention may be applied in the field ofrenewable wind energy. The apparatus may be configured and incorporatedinto wind turbines to facilitate monitoring and adjustment thereof, forexample as a safety and performance enhancement sensor. One or more ofthe outputs of the apparatus may be used for pitch blade adjustment,and/or force safety sensors. Embodiments of the present invention may beconfigured to support oscillating wind technology, also known as vortexwind turbines.

Embodiments of the present invention may be applied in the field ofaviation, for example providing a sensor for use by private andrecreational pilots. The apparatus may be incorporated into lightaircraft, gliders, unmanned aerial vehicles, and/or as a backup sensor.

For example, light aircraft often rely on a single pitot-tube sensor.This sensor often does not have a backup system. If the pitot-tubesensor becomes obstructed or damaged, it can lead the pilot to a stallsituation. The majority of crashes happen on the landing approach whenreported speeds are incorrect. Hang gliding also has potential to stall,or worst have a “Whip Kick” or Whip Stall”, which is dangerous and oftenends in a crash. The present invention may be configured to emit awarning signal upon detection of incipient stall conditions.

Through the descriptions of the preceding embodiments, the presentinvention may be implemented by using hardware only or by using softwareand a necessary universal hardware platform. Based on suchunderstandings, the technical solution of the present invention may beembodied in the form of a software product. The software product may bestored in a non-volatile or non-transitory storage medium, which can bea compact disk read-only memory (CD-ROM), USB flash disk, or a removablehard disk. The software product includes a number of instructions thatenable a computer device (personal computer, server, or network device)to execute the methods provided in the embodiments of the presentinvention. For example, such an execution may correspond to a simulationof the logical operations as described herein. The software product mayadditionally or alternatively include number of instructions that enablea computer device to execute operations for configuring or programming adigital logic apparatus in accordance with embodiments of the presentinvention.

Although the present invention has been described with reference tospecific features and embodiments thereof, it is evident that variousmodifications and combinations can be made thereto without departingfrom the invention. The specification and drawings are, accordingly, tobe regarded simply as an illustration of the invention as defined by theappended claims, and are contemplated to cover any and allmodifications, variations, combinations or equivalents that fall withinthe scope of the present invention.

We claim:
 1. A method for calibrating a multi-hole pivot probe windsensor, comprising: receiving an indication of a body proximate to theprobe; estimating a flow field induced by the presence of the body atleast in the vicinity of the probe; performing computations related to asuperposition of the estimated flow field onto another flow field forthe probe; estimating a measurement error induced in the probe by thebody, the estimate based on the superposition; and providing acorrection factor for at least partially countering the measurementerror.
 2. The method of claim 1, wherein the indication of the bodyincludes an indication of one or both of: distance between the body andthe probe; and configuration of the body relative to the probe, andwherein the indication is provided using one or more sensors.
 3. Themethod of claim 1, wherein the method is repeated for multipleconfigurations of the body relative to the probe.
 4. The method of claim3, wherein, for each one of the multiple configurations of the body, theestimated flow field is obtained via experimental measurements performedon the body in said one of the multiple configurations.
 5. A method foroperating a multi-hole pitot probe wind sensor mounted to a surfacevehicle, comprising: receiving an indication of shape or relativelocation of a body proximate to the probe; and providing a correctionfactor to be applied to measurements from the probe based on thereceived indication, wherein the wind sensor is configured for measuringvelocity and angle of wind relative to the surface vehicle and whereinthe correction factor is applied to said measurements of velocity andangle of wind.
 6. The method of claim 5, wherein the indication isreceived from one or more sensors.